Concept

Duality (optimization)

Related lectures (31)

Covers weak and strong duality in optimization problems, focusing on Lagrange multipliers and KKT conditions.

Linear Optimization: Finding Initial BFS

Explains the process of finding an initial Basic Feasible Solution for linear optimization problems using the Simplex Algorithm.

Linear Programming: Two-phase Simplex Algorithm

Covers the application of the two-phase Simplex algorithm to solve linear programming problems.

Lagrangian Duality: Convex Optimization

Explores Lagrangian duality in convex optimization, transforming problems into min-max formulations and discussing the significance of dual solutions.

Optimal Decision Making: Sensitivity Analysis

Covers sensitivity analysis in linear programming, focusing on optimal solutions and their sensitivities to changes.

Convex Optimization: Generalized Inequalities

Explores problems with generalized inequalities in convex optimization and the equivalence between SOCP and SDP.

Lagrangian Duality: Theory and Applications

Explores Lagrangian duality in convex optimization, discussing strong duality, dual solutions, and practical applications in second-order cone programs.

Primal-dual optimization: Theory and Computation

Explores primal-dual optimization, conjugation of functions, strong duality, and quadratic penalty methods in data mathematics.

Primal-dual Optimization: Fundamentals

Explores primal-dual optimization, minimax problems, and gradient descent-ascent methods for optimization algorithms.

Linear Programming Duality

Covers linear programming duality and complementary slackness condition.

Optimality Conditions in Linear Optimization

Covers optimality conditions, strong duality, and complementarity slackness in linear optimization.

Linear Optimization: Auxiliary Problem

Explores the formulation of the auxiliary problem in linear optimization and its role in optimal decision-making.

Duality: Economic Interpretation

Explores duality in linear programming, strong duality, complementary slackness, and the economic interpretation of dual variables as prices.

Convex Optimization Tutorial: KKT Conditions

Explores KKT conditions in convex optimization, covering dual problems, logarithmic constraints, least squares, matrix functions, and suboptimality of covering ellipsoids.

Linear Models for Classification

Covers linear models for classification, including SVM, decision boundaries, support vectors, and Lagrange duality.

Duality: Lagrangian and Dual Problem

Covers Lagrangian, dual function, dual problem, weak duality, and optimality.

Duality in Linear Programming

Explores the concept of duality in linear programming, discussing the relationship between primal and dual problems.

Linear Programming Duality

Explores linear programming duality, covering constraints, variables, solutions, and the relationship between primal and dual LP.

Conjugate Duality: Envelope Representations and Subgradients

Explores envelope representations, subgradients, and the duality gap in convex optimization.

Optimization Duality: Theory and Algorithms

Explores optimization duality, weak and strong duality, practical optimization algorithms, and challenges in nonconvex-concave problems.